Chest Bone Moves Unwantedly With the Hip Bone
You appear to be using the initial metarig which rigify provides for you to scale and position to suit your character. After positioning this rig to your model you should then generate the animation friendly rig.

The initial metarig -



The generate button is available in the armature properties



The animation rig that gets generated -



Notice that when the final rig is active it displays a rig layers panel in the properties sidebar (press N) and while in pose mode a rig properties panel is available showing properties of the selected bones.

CGCookie has a tutorial on using the rigify addon that demonstrates the steps needed to use rigify.